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Full text of "Mathematical And Physical Papers - Iii"

40    ON THE EFFECT OF THE IKTEENAL FBICTION OF FLUIDS
27.    Let a be the radius of the cylinder ; and as before let the cylinder's motion be defined by the equation
c^'** ....................... (78);
then we have for the equations of condition which relate to the surface of the cylinder
dt                                                     ,
,                              whenr=a...(79).
~^ dr               dt                         }
The general equations (75), (76), as well as the equations of condition (79), may be satisfied by taking
%i = &H sin 6 F (r),   ^ = &'**' sin (9 ^ (r) ......... (80).
Substituting in (75), (76), and (79), we get
F:(r)+^(r)Fz(r)-m^(r) = 0 ......... (82),
JT1(a) + JT2(a) = ac,   J/ (a) + F9f (a) = c ............ (83),
besides which we have the condition that the velocity shall vanish at an infinite distance.
28.   The integral of (81) is
F^^ + Br  ........................ (84).
The integral of (82) cannot be obtained in finite terms.
To simplify the latter equation, assume J?2 (r) = FB' (r).    Substituting in (82), and integrating once, we get
(85).
It is unnecessary to add an arbitrary constant, because such a constant, if introduced, might be got rid of by writing F (r) + G